As a (transplanted) South Sounder, I'd like to chime in a bit. If you have more than a day or so, there are some great things to do down here in the South Sound area.
Mount Rainier is wonderful if you have the time to make the drive. It will take all day - it does from my house and I'm an hour south of Seattle. Paradise is a good destination.
NorthWest Trek was mentioned - this is a wonderful zoo. All animals from the NW so if you really wanted to see that moose or bear, you can catch them here. They have a tram ride through the free roaming section that is great.
Point Defiance Zoo in Tacoma is a nice zoo (I like NW Trek better) but there are some other fun stuff at Point Defiance Park: Fort Nisqually, a trading post from the Hudson Bay Company days, a logging museum complete with train ride, a Japanese garden and plenty of walking trails.
One more animal thing: Wolf Haven, International just south of Olympia. A rescue center for wolves and wolf/dog breeds, they do a great job advocating for their animals. You get an hour-long guided tour here and get to see the wolves do what they do. When we went they were howling as we got out of our cars. Amazing.
There are a few train rides out here for the train buffs - Snoqualmie/North Bend has a train. That's up off of I-90 to the east of Seattle. Chehalis has a steam train that does runs, which is south of Olympia. Mount Rainier Scenic Railway also does runs near (but not into) Mount Rainier National Park. Yes, we have a train fan in our house and have done all three.
The Glass Museum in Tacoma is very nice, as is the Tacoma Art Museum. They are close to each other and could easily be done together. The Washington State History museum is also nearby. My kids love this one. Don't be scared of Tacoma. I have managed to navigate and visit it multiple time with just me and my kids in the last three years and have always been fine.
Both Tacoma and Olympia have children's museums that are getting new buildings this year. They were good in the past, should be better in the new buildings.
Mount St. Helens is an absolute favorite of our family. We have been many times and visited both the state visitor's center at the bottom and federal one at the highest overlook. Both are well done. It's something you have to see to appreciate. It's a long drive from Seattle (again, it takes us a full day and we're an hour south) but if you have time and a car, it's worth it. One caveat, be sure you can see the volcano from Johnston Ridge before you head that way. Their website has a webcam so you can check. If there are clouds up there you will not be able to see Mount St Helens at all.
If Navy ships are your thing, there is the USS Turner Joy in Bremerton. It's a Vietnam era destroyer. You can take the ferry from Seattle to Bremerton.
I'd also like to say don't skip the Space Needle if you want to do it. It's fun. It's Seattle. IF you have a nice day, the views are nice. You can also go up at night if your time is tight. Parents do be forewarned about the carnival rides at the bottom. Your kids will want to ride them.
I'd also like to add my recommendation for the Gold Rush Museum near Pioneer Square. It is fairly new and was very well done. My DD8 and DS4 both enjoyed it, as did my DH and I. They have the best Junior Ranger books I have ever seen and we do these frequently. Staff couldn't have been nicer and we all learned something.
Sorry this is long but thought I'd throw some other things out there for those with more days. We're excited about our cruise in July. Family coming out and joining us for this one. Now if I can just figure out the best way to get 9 people and their gear from my house in the south to the terminal without having to drive and park both cars there, I'd be getting somewhere.
